BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Leonid Parnovski (UCL) DTSTART:20240617T131500Z DTEND:20240617T140000Z DTSTAMP:20260423T021151Z UID:MAS-MP/77 DESCRIPTION:Title: Spectral asymptotics for the Schrödinger operator with bounded\, unstruct ured potentials.\nby Leonid Parnovski (UCL) as part of Munich-Copenhag en-Santiago Mathematical Physics seminar\n\n\nAbstract\nHigh energy spectr al asymptotics for Schrödinger operators on compact manifolds have been w ell studied since the early 1900s and it is now well known that they are i ntimately related to the structure of periodic geodesics. In this talk\, w e discuss analogous questions for Schrödinger operators on $R^d$ with pot entials bounded together with all their derivatives. Since the geodesic fl ow on $R^d$ has no periodic trajectories (or indeed looping trajectories) one might guess that the spectral projector has a complete asymptotic expa nsion in powers of the spectral parameter. We show that when $d=1$\, this is indeed the case. When $d=2$\, we give a large class of potentials whose spectral projectors have complete asymptotics. Nevertheless\, in $d\\ge 2 $\, we construct examples where complete asymptotics fails. \nBased on joi nt work with J. Galkowski and R. Shterenberg\n LOCATION:https://researchseminars.org/talk/MAS-MP/77/ END:VEVENT END:VCALENDAR